A hybrid preconditioner of banded matrix approximation and alternating direction implicit iteration for symmetric Sinc-Galerkin linear systems

doi:10.1016/S0024-3795(02)00502-5

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	A hybrid preconditioner of banded matrix approximation and alternating direction implicit iteration for symmetric Sinc-Galerkin linear systems
	Ng, MK ; Bai, ZZ
	2003-06-01
发表期刊	LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN	0024-3795
卷号	366 页码:317-335
摘要	The symmetric Sinc-Galerkin method applied to a sparable second-order self-adjoint elliptic boundary value problem gives rise to a system of linear equations (Psi(x) circle times D-y + D-x circle times Psi(y))u = g, where circle times is the Kronecker product symbol, Psi(x) and Psi(y) are Toeplitz-plus-diagonal matrices, and D-x and D-y are diagonal matrices. The main contribution of this paper is to present and analyze a two-step preconditioning strategy based on the banded matrix approximation (BMA) and the alternating direction implicit (ADI) iteration for these Sinc-Galerkin systems. In particular, we show that the two-step preconditioner is symmetric positive definite, and the condition number of the preconditioned matrix is bounded by the convergence factor of the involved ADI iteration. Numerical examples show that the new preconditioner is practical and efficient to precondition the conjugate gradient method for solving the above symmetric Sinc-Galerkin linear system. (C) 2003 Elsevier Science Inc. All rights reserved.
关键词	Toeplitz-plus-diagonal ADI banded preconditioner
DOI	10.1016/S0024-3795(02)00502-5
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000182667200018
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/18110
专题	中国科学院数学与系统科学研究院
通讯作者	Ng, MK
作者单位	1.Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Sate Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Ng, MK,Bai, ZZ. A hybrid preconditioner of banded matrix approximation and alternating direction implicit iteration for symmetric Sinc-Galerkin linear systems[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,2003,366:317-335.
APA	Ng, MK,&Bai, ZZ.(2003).A hybrid preconditioner of banded matrix approximation and alternating direction implicit iteration for symmetric Sinc-Galerkin linear systems.LINEAR ALGEBRA AND ITS APPLICATIONS,366,317-335.
MLA	Ng, MK,et al."A hybrid preconditioner of banded matrix approximation and alternating direction implicit iteration for symmetric Sinc-Galerkin linear systems".LINEAR ALGEBRA AND ITS APPLICATIONS 366(2003):317-335.